Question

The radius and height of a circular cone in the ratio of 3:4 if its volume is 301.44 cm cube find the radius and the slant height of the cone .(take pie =3.14)​

Answer 1

Answer: radius = 6 cm, slant height = 10 cm

Step-by-step explanation:

Answer 2

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Let the radius,height = 3x,4x

Volume=301.44

$\star \;{\underline{\boxed{\purple{\pmb{\pmb{ \pmb{\textbf{\textsf{ To\;Find \; :- }}}}}}}}}$

$\begin{gathered} \\\end{gathered}$

Radius = ?

Height = ?

$\begin{gathered}\begin{gathered} \\ \qquad{\rule{200pt}{2pt}} \end{gathered}\end{gathered}$

$\begin{gathered} \\ \\\end{gathered}$

$\begin{gathered} \\\end{gathered}\star \;{\underline{\boxed{\red{\pmb{\pmb{\pmb{\textbf{\textsf{ SoluTion \; :- }}}}}}}}}$

$\quad{ \frak{ \underline { \red{ \bold{ \frak{Formula \: used:} }}}}}$

${\underline{\boxed{\pmb{\pmb{\sf{ \: \sf \:Volume_{(Cone)}=\dfrac{1}{3}×\dfrac{22}{7}×r^2×h  }}}}}}$

$\begin{gathered}\begin{gathered} \\ \end{gathered}\end{gathered}\begin{gathered}\begin{gathered} \\ \\\end{gathered}\dag \;{\underline{\underline{\sf{ \; Calculating \; the \; Radius }}}}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)}=\dfrac{1}{3}×\dfrac{22}{7}×r^2×h } \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)}=\dfrac{1}{3}×\dfrac{22}{7}×3x^2×4x = 301.44 } \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)} = 36x {}^{3} = 301.44 \times 3 \times \dfrac{7}{22} } \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)} = 36x {}^{3} = 287.73} \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)} = x {}^{3} = \dfrac{287.7}{36} } \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)} = x {}^{3} = 8} \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)} = x = \sqrt[3]{} 8} \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \; \longmapsto \; \sf {Volume_{(Cone)} = x = 2} \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \\ \qquad{\rule{200pt}{2pt}} \end{gathered}\end{gathered}$

${\pmb{\pmb{\pmb{\pmb{}}}}}$

Hence,radius of cone is 6cm and height is 8cm.

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